Symplectic implosion and non-reductive quotients

Details Symplectic implosion and non-reductive quotients Symplectic implosion and non-reductive quotients

2008-12-15

arxiv.org/abs/0812.2782v1

Mathematics

Algebraic Geometry

For the proceedings of the 65th birthday conference for Hans Duistermaat, Utrecht 2007

Scientific paper

The symplectic implosion construction of Guillemin, Jeffrey and Sjamaar associates to a Hamiltonian action of a compact group K on a symplectic manifold X its 'imploded cross section'. When X is a complex projective variety and K acts linearly on X, this construction is closely related to geometric invariant theory (GIT) for the action on X of a maximal unipotent subgroup U of the complexification G of K. The aim of this paper is to generalise symplectic implosion to give a symplectic construction for GIT-like quotients by unipotent radicals U of arbitrary parabolic subgroups P of the complex reductive group G acting linearly on the projective variety X.

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